CHLa and DIN Time Series Plots




Summary Statistics by Year

James River Station JMS75 Mean Water Quality Values, by Year
Means based on values observed during July-October index period
Year Dischargea Discharge_sampling SurfaceTempb CHLac DINd SpConde CHLa_90th
2010 59.97 39.70 25.95 90.27 0.20 559.22 111.30
2011 108.93 88.05 25.73 46.61 0.23 254.34 64.10
2012 58.72 61.88 25.89 36.04 0.14 308.49 42.10
2013 164.37 150.34 24.71 27.26 0.27 197.81 35.91
2014 66.08 61.39 25.74 39.04 0.13 307.61 43.78
2015 124.32 71.69 25.58 57.35 0.15 243.50 75.20
2016 117.50 130.52 26.62 35.32 0.23 212.77 53.53
2017 47.47 44.56 25.85 49.87 0.07 323.82 63.03
2018 320.86 341.28 26.54 18.41 0.22 149.91 29.27
2019 73.21 73.70 26.66 50.94 0.04 332.29 63.48
2020 189.48 208.44 25.48 39.20 0.19 150.97 51.75
2021 108.04 91.10 26.61 42.29 0.15 198.28 57.21
2022 67.30 73.87 25.72 24.22 0.06 274.84 35.36
2023 94.09 108.73 26.06 32.05 0.10 228.88 47.81
a m³/s
b Celsius
c μg/L
d mg/L
e μS/cm



Counts of Algal Bloom, N-Depleted, and Low Flow Days, Jul-Oct 2010-2023
Year Bloom daysa N-depleted daysb Low.flow.daysc
2010 91 28 112
2011 56 21 88
2012 21 28 117
2013 7 14 58
2014 77 21 116
2015 63 35 84
2016 56 28 69
2017 70 70 120
2018 14 35 29
2019 91 105 93
2020 42 35 38
2021 63 21 82
2022 14 84 112
2023 28 77 91
a CHLa > 40 μg/L
b DIN < .07 mg/L
c discharge < 100 m³/s



Model 1: CHLa ~ Temperature/Discharge Ratio


Regression Plots





Regression Statistics

Regression statistics by year for ln(CHLAa) ~ ln(T:Q)
Model.Year coefficient coef.error p.val RSQR
All years 0.7504 0.0219 0 0.6933
2010 0.7319 0.0804 0 0.8115
2011 0.6987 0.0742 0 0.6922
2012 0.6626 0.0690 0 0.7006
2013 0.8127 0.0914 0 0.6670
2014 0.6436 0.0430 0 0.8351
2015 0.8628 0.0811 0 0.7372
2016 0.8651 0.0719 0 0.8134
2017 0.5156 0.0883 0 0.4590
2018 0.9514 0.1174 0 0.6487
2019 0.8511 0.0667 0 0.8180
2020 0.8064 0.0855 0 0.7274
2021 0.7713 0.0556 0 0.8342
2022 0.5786 0.0894 0 0.5184
2023 0.8028 0.1082 0 0.6211



Model Performance and Residuals Plots


Model Result Count Percentage
correctly predicted 415 80%
false negative 64 12%
false positive 40 8%







Model 2: CHLa ~ Temperature/Discharge 4day Moving Avg. Ratio


Regression Plots






Regression Statistics

Regression statistics by year for ln(CHLAa) ~ ln(T/Qavg)
Model.Year coefficient coef.error p.val RSQR
All years 0.7624 0.0216 0 0.7055
2010 0.7033 0.0831 0 0.7880
2011 0.7246 0.0611 0 0.7815
2012 0.6589 0.0733 0 0.6716
2013 0.7757 0.0867 0 0.6698
2014 0.6411 0.0383 0 0.8636
2015 0.8602 0.0827 0 0.7283
2016 0.8443 0.0797 0 0.7710
2017 0.5085 0.0838 0 0.4790
2018 1.0344 0.1024 0 0.7426
2019 0.9266 0.0646 0 0.8505
2020 0.8786 0.0790 0 0.7879
2021 0.8378 0.0600 0 0.8364
2022 0.5961 0.0808 0 0.5847
2023 0.8185 0.1063 0 0.6385



Model Performance and Residuals Time Series

Model Result Count Percentage
correctly predicted 416 80%
false negative 63 12%
false positive 40 8%





Model 3: CHLa ~ Temperature/Inverse Special Conductivty Ratio


Regression Plots





Regression Statistics

Regression statistics by year for ln(CHLAa) ~ ln(T:InvSpCond)
Model.Year coefficient coef.error p.val RSQR
All years 1.1659 0.0367 0 0.6639
2010 0.7607 0.0940 0 0.7726
2011 1.2887 0.0846 0 0.8589
2012 0.9953 0.1153 0 0.6591
2013 1.2783 0.1385 0 0.6833
2014 0.9326 0.0688 0 0.8096
2015 1.2686 0.1098 0 0.7770
2016 1.3741 0.1510 0 0.7188
2017 0.8939 0.1438 0 0.4977
2018 1.3544 0.2324 0 0.4851
2019 1.4557 0.1153 0 0.8148
2020 1.5264 0.1872 0 0.6649
2021 1.3641 0.1146 0 0.7873
2022 0.9407 0.1261 0 0.5900
2023 1.5481 0.1879 0 0.6696



Model Performance and Residuals Time Series

Model Result Count Percentage
correctly predicted 410 80%
false negative 74 14%
false positive 28 5%





Model 4: Nonlinear Tangential Model


\[CHLa \sim CHLamax \times \tanh\left(\frac{\alpha \times T}{CHLamax}\right)\]






Parameter Estimates

CHLa ~ CHLamax * tanh((alpha * t_q)/CHLamax) Model Statistics, by Year
Model.Year alpha.coef alpha.p.val alpha.se CHLamax.coef CHLamax.pval CHLamax.se
All years 179.8142 0.0000 10.0221 54.5534 0.0000 2.1946
2010 324.8052 0.0010 82.7163 98.4683 0.0000 8.3391
2011 171.5873 0.0000 17.8594 70.3725 0.0000 6.5894
2012 184.1062 0.0000 33.6773 37.1384 0.0000 3.7209
2013 200.5209 0.0000 31.6942 34.2064 0.0000 4.0911
2014 161.7570 0.0000 18.1576 42.4314 0.0000 2.6866
2015 201.6760 0.0000 32.9805 89.9767 0.0000 16.6996
2016 262.7959 0.0000 46.7359 49.5614 0.0000 4.7956
2017 299.0963 0.0029 93.9749 46.0346 0.0000 5.3498
2018 108.9656 0.0000 16.4727 52.3080 0.0276 22.7181
2019 165.8154 0.0000 23.8216 62.8194 0.0000 6.3599
2020 359.2150 0.0000 41.2794 52.5422 0.0000 4.2538
2021 200.2345 0.0000 28.8275 52.3470 0.0000 6.4961
2022 187.6288 0.0005 49.2655 24.9221 0.0000 2.4902
2023 253.3101 0.0004 64.6124 33.5362 0.0000 3.0208



Model Performance and Residuals Time Series



Model Result Count Percentage
correctly predicted 182 35%
false positive 337 65%